I'm trying to figure out what the Livonian character ȱ sounds like. As far as I can tell, it's a long mid-high unrounded back vowel. In IPA it seems to be written as /ɤː/
but that seems to be a non-standard IPA form?
The symbol [ɤː] is the correct one for the sound you describe and is a standard IPA symbol (although it's not a super-common vowel in the world's languages, but does crop up here and there).
There is also the near-high (as opposed to high-mid) back rounded vowel [ʊ]; perhaps this is what you were expecting?
As for what these sound like, have a look at this website: http://www.ipachart.com/.
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3Although the English Wikipedia article says ȯ in Livonian represents [ʊ], the Latvian article, which is substantiated with more sources, says it's either [ɤ] or [ɤ̞]. – Nardog Feb 3 '19 at 13:03
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I was under the impression that [ʊ] is near-back by default; is that not the case? – snorepion Feb 3 '19 at 17:00
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1That is indeed what it is called on page 170 of the Handbook of the IPA; I was just trying simplify things a little (and in any case it does also get used for back as well as near-back near-high rounded vowels). – Miztli Feb 3 '19 at 20:00